A witch or wizard who supposedly has magical blood on both sides of the family going back generations.

Pure-blood status is somewhat of a myth, since nearly all Wizarding families have mingled with Muggles at some point in their history (CS7)

Pureblood - families are listed in a book called the "The Pure-blood Directory," which lists the "Sacred Twenty-eight" families (Pm)

The tapestry of the Black Family tree at Grimmauld Place showed empty burn holes where anyone who married a Muggle or Muggleborn was blasted off (OP6).

While Harry Potter had a witch and a wizard as parents, he was still considered a Half-Blood by Voldemort and the Death Eaters due to the fact that his mother Lily was Muggleborn. Purity must go back many generations to be acceptable (CS17, JKR). Harry's father James Potter was a pure-blood from an old illustrious magical family, but they were not listed in the Sacred Twenty-eight due to possibly tainted blood (Pm).

While Slytherin House is associated with pure-blood status due to the prejudices of the founder, Salazar Slytherin, it is not a requirement. In fact, Head of Slytherin Severus Snape was a Half-Blood (Pm, HBP2, HBP28, DH33).

The Weasley Family is listed on the Sacred Twenty-eight, but they are considered blood-traitors for sympathizing with Muggles (OP6).